Amplitude domain approach to digital filtering: Theory and applications of L-filters: Dissertation

The thesis proposes several new ideas concerning order statistic based percentile estimation and introduces extensions of these ideas to the use in signal and image processing. One important goal of this thesis is to give a unified presentation of the theory of L-filters including their statistical background. The presentation demonstrates how L-filters can be exploited to solve practical problems by introducing algorithms and implementations together with application examples. The thesis introduces several original results both theoretical and practical. Among them are the concept of subset averaging including subset averaged median estimator (SAME), subset averaged percentile estimator (SAPE) and subset averaged scale estimator (SAPE-dif). Proposed subset averaged estimators are applied to image processing to create a new class of order statistic based image restoration filters. Furthermore, some application related results are presented such as the L-filter structure for image enhancement, L-filter based monitoring of the shape of a distribution, L-filter bank algorithm for running probability density function estimation, new concept and implementation of ultrasonic sonar for environment perception and presentation of multiresolution histogram algorithm together with hardware realization. To obtain a unified presentation three approaches are emphasized: amplitude domain approach, robustness instead of optimality and the existence of a vital link between statistical theories and signal processing procedures. The thesis contains an extensive case study with comparisons of all major L-estimators together with proposed methods. Comparisons are carried out concerning both steady state and transient behavior of L-filters. Presented comparisons are aimed to offer a profound insight into the overall behavior, performance and robustness of both L-estimators and L-filters.